library(aplore3)
library(ggplot2)
library(plotly)
library(RColorBrewer)
library(pheatmap)
library(cluster)

Data Format: A data.frame with 500 rows and 18 variables such as:

priorfrac - If the patient previously had a fracture
age
weight
height
bmi
premeno
momfrac
armassist
smoke
raterisk
fracscore
fracture
bonemed - Bone medications at enrollment (1: No, 2: Yes)
bonemed_fu - Bone medications at follow-up (1: No, 2: Yes)
bonetreat - Bone medications both at enrollment and follow-up (1: No, 2: Yes)

head(glow_bonemed)
##   sub_id site_id phy_id priorfrac age weight height      bmi premeno momfrac
## 1      1       1     14        No  62   70.3    158 28.16055      No      No
## 2      2       4    284        No  65   87.1    160 34.02344      No      No
## 3      3       6    305       Yes  88   50.8    157 20.60936      No     Yes
## 4      4       6    309        No  82   62.1    160 24.25781      No      No
## 5      5       1     37        No  61   68.0    152 29.43213      No      No
## 6      6       5    299       Yes  67   68.0    161 26.23356      No      No
##   armassist smoke raterisk fracscore fracture bonemed bonemed_fu bonetreat
## 1        No    No     Same         1       No      No         No        No
## 2        No    No     Same         2       No      No         No        No
## 3       Yes    No     Less        11       No      No         No        No
## 4        No    No     Less         5       No      No         No        No
## 5        No    No     Same         1       No      No         No        No
## 6        No   Yes     Same         4       No      No         No        No
summary(glow_bonemed)
##      sub_id         site_id          phy_id       priorfrac      age       
##  Min.   :  1.0   Min.   :1.000   Min.   :  1.00   No :374   Min.   :55.00  
##  1st Qu.:125.8   1st Qu.:2.000   1st Qu.: 57.75   Yes:126   1st Qu.:61.00  
##  Median :250.5   Median :3.000   Median :182.50             Median :67.00  
##  Mean   :250.5   Mean   :3.436   Mean   :178.55             Mean   :68.56  
##  3rd Qu.:375.2   3rd Qu.:5.000   3rd Qu.:298.00             3rd Qu.:76.00  
##  Max.   :500.0   Max.   :6.000   Max.   :325.00             Max.   :90.00  
##      weight           height           bmi        premeno   momfrac   armassist
##  Min.   : 39.90   Min.   :134.0   Min.   :14.88   No :403   No :435   No :312  
##  1st Qu.: 59.90   1st Qu.:157.0   1st Qu.:23.27   Yes: 97   Yes: 65   Yes:188  
##  Median : 68.00   Median :161.5   Median :26.42                                
##  Mean   : 71.82   Mean   :161.4   Mean   :27.55                                
##  3rd Qu.: 81.30   3rd Qu.:165.0   3rd Qu.:30.79                                
##  Max.   :127.00   Max.   :199.0   Max.   :49.08                                
##  smoke        raterisk     fracscore      fracture  bonemed   bonemed_fu
##  No :465   Less   :167   Min.   : 0.000   No :375   No :371   No :361   
##  Yes: 35   Same   :186   1st Qu.: 2.000   Yes:125   Yes:129   Yes:139   
##            Greater:147   Median : 3.000                                 
##                          Mean   : 3.698                                 
##                          3rd Qu.: 5.000                                 
##                          Max.   :11.000                                 
##  bonetreat
##  No :382  
##  Yes:118  
##           
##           
##           
##

Age vs Weight: As weight increases the average age decreases
Age vs Height: Weak correlation of as height increases age decreases
Age vs BMI: As bmi increases the average age decreases
Age vs fracscore: As age increases the average fracscore increases

Weight vs Height: As height increases the average weight increases
Weight vs BMI: As bmi increases the average weight increases
Weight vs fracscore: As fracscore increases the average Weight decreases

Height vs BMI: As bmi increases the average height and variance stay the same
Height vs fracscore: As fracscore increases the average height stays the same though variance might decrease

BMI vs fracscore: As fracscore increases the average bmi decreases

plot(glow_bonemed[, c(5:8, 14)])

Non of the following scatter plots show strong groupings for the fracture/no fracture categorical variable

ggplot(glow_bonemed, aes(x = age, y = bmi, color = fracture)) +
  geom_jitter()+
  labs(title = "BMI vs Age")

ggplot(glow_bonemed, aes(x = bmi, y = fracscore, color = fracture)) +
  geom_jitter()+
  labs(title = "Fracture Score vs BMI")

ggplot(glow_bonemed, aes(x = fracscore, y = age, color = fracture)) +
  geom_jitter()+
  labs(title = "Age vs Fracture Score")

ggplot(glow_bonemed, aes(x = weight, y = height, color = fracture)) +
  geom_jitter()+
  labs(title = "Height vs Weight")

Once again there doesn’t seem to be strong groupings of the fracture categorical variable

fracture3dplot = plot_ly(glow_bonemed, 
  x = ~age, 
  y = ~height, 
  z = ~bmi, 
  color = ~fracture, 
  colors = c('#0C4B8E', '#BF382A')) %>% add_markers()

fracture3dplot

The boxplot shows that the mean fracscore seems to be slightly higher for smokers compared to non smokers

ggplot(glow_bonemed, aes(x = smoke, y = fracscore)) +
  geom_boxplot()+
  labs(title = "Fracture Score Summary Statistics for Smokers vs Non Smokers")

Clustering EDA

pheatmap(glow_bonemed[, c(5,8)], scale = "column", fontsize_row = 0.1, cluster_cols = F, legend = T, color = colorRampPalette(c("blue", "white", "red"), space = "rgb")(100))

pheatmap(glow_bonemed[, 5:8], scale = "column", fontsize_row = 0.1, cluster_cols = F, legend = T, color = colorRampPalette(c("blue", "white", "red"), space = "rgb")(100))

zScoreScale = scale(glow_bonemed[, 5:8])

zScoreDistance = dist(zScoreScale)

continuousVariableClustering = hclust(zScoreDistance, method = "complete")

plot(continuousVariableClustering)

Sources:
Hosmer, D.W., Lemeshow, S. and Sturdivant, R.X. (2013) Applied Logistic Regression, 3rd ed., New York: Wiley

https://cran.r-project.org/web/packages/aplore3/aplore3.pdf#page=11&zoom=100,132,90